B – Stochastic systems and continuum limits
Mathematical modeling for complex systems in regimes between discrete and continuum plays a central role in the whole CRC. Depending on the respective problem, the challenge is the transition from finite to infinite numbers of particles (or dimensions or other parameters) or from infinite but discrete to con- tinuous models. Starting from well understood, simplified microscopic models and basic principles one aims to identify a family of statistics which resume the main features on the global scale. This allows to abstract from the detailed microscopic modeling and to gain a canonical macroscopic description. For numerous phenomena in nature and sciences, discrete probabilistic models (e.g. lattice models, point processes, or random walks in a random environment) provide the easiest and most efficient mathematical description. On the other hand, many evolution processes in nature or society are classically described in terms of PDEs, transport problems, gradient flows, or discrete propagation schemes but frequently it is adequate to include stochastic noise terms. The Project Group B will focus on stochastic systems and their continuum limits.
B01 Metastability (Bovier)
B02 Ageing and slow dynamics (Bovier)
B03 Optimal transport and random measures (Sturm)
B04 Random matrices and random surfaces (Ferrari, Peltola)
B05 Dynamics of coagulation-fragmentation equations (Niethammer, Velázquez)
B08 Screening and long-range interactions in problems in materials science (Niethammer, Velázquez)